The two-dimensional stiffened plate problem is completely governed by the fundamental differential equation

(22)

where k1 and k2 are two non-dimensional structural constants depending on the relative proportions of the reinforcing members.

The complete solution is

(25)

This solution renders all solutions for the isotropic plate available for the stiffened plate also. The choice between the several types of solution available is governed by the same considerations as for the isotropic or unstiffened plate.

This paper has been compiled because of the applicability of the treatment of the stability of the motion of the common spinning top to the problem of the whirling of rotating shafts, carrying loads of appreciable moments of inertia. This problem is assuming renewed interest and importance, especially in the drives of contra-propeller systems and the more recent high speed prime movers.

Performance measurements for turbo-jet and turbo-prop aircraft are most conveniently reduced to standard conditions by the use of graphical methods. The case of rate of climb presents difficulties if readings are taken in the normal way during continuous climbs, because of the variation of weight, temperature, pressure and optimum climbing speed with height.

Since rate of climb is proportional to the product of speed and acceleration in level flight, these quantities could be measured and used to determine the rate of climb at any height.

The advantages of the method are listed and the technique required of the pilot examined. An automatic observer, including a longitudinal accelerometer, reading, in some cases, to within 0.001g, is necessary.

A linearised theory for the subsonic, lifting surface problem is formulated in terms of Fourier integral solutions to Laplace’s equation. The symmetric and anti-symmetric problems of the first kind are solved explicitly, while the problems of the second kind depend on the solution of dual integral equations. The antisymmetric problem of the second kind is cast in a variational form, from which certain well-known theorems may be deduced.

In the previous linearised theories of steady supersonic flow past a slender oscillating aerofoil, the shock line at the nose has been assumed to be a straight, stationary one, so that no vorticity is produced on passing through it. In the present treatment, the possibility that the shock may be both curved and moving is taken into account, but the result is exactly the same as that obtained by the previous treatments (e.g. Temple and Jahn).

In many important problems of supersonic flow, either for the whole field of flow or a part of it, the velocity components are constant on straight lines through a fixed point. Such velocity fields are called conical fields. In the usual theory of the linearised perturbations of a steady supersonic flow, the velocity is assumed to differ only slightly from a uniform undisturbed velocity, and in the defining equations and boundary conditions all non-linear terms in the components of the perturbation velocity (and their space derivatives) are neglected. In this paper the equations of linearised supersonic conical fields, and their general solution, are set out both for the region inside and for the region outside the Mach cone of the origin in the conical field. The results are applied to flow past plane triangular aerofoils with straight edges downstream of the vertex (of which there are six cases), to flow past those plane aerofoils of more extended shape and finite span for which the solution may be obtained by combining a finite number of conical fields, and to the problem of plane triangular vanes in semi-infinite free jets. In the applications, the velocity fields are determined in considerable detail, but a main purpose in setting them out was to exhibit the mathematical methods used and the physical considerations that enter in determining the mathematical solutions.